proof of Ingham Inequality
If is a integrable function in , let
It is easy to prove the equalities.
For the rest of the proof we make the following choices:
Then, after computation, we have
Let and (). Since , we have that . If we suppose that is fixed, we have
But, since and , we find
where . Using the definition of and the previous inequality, we have
and we have obtained the conclusion.
|Title||proof of Ingham Inequality|
|Date of creation||2013-03-22 15:55:18|
|Last modified on||2013-03-22 15:55:18|
|Last modified by||ncrom (8997)|